Question

7 find the area of each sector. answer correct to one decimal place.
a
b
c
d
e
f

Explanation:

Identify the sector area formula

Using the Circle Area knowledge point
The area of a sector with radius \(r\) and central angle \(\theta^\circ\) is given by:

$$ A = \frac{\theta}{360} \times \pi r^2 $$

Calculate areas for sectors a, b, and c

Using the Circle Area knowledge point

• Sector a: Semicircle with \(r = 3\text{ cm}\), \(\theta = 180^\circ\).

$$ A_a = \frac{180}{360} \times \pi \times 3^2 = 4.5\pi \approx 14.137 \approx 14.1\text{ cm}^2 $$

• Sector b: Sector with \(r = 10\text{ cm}\), \(\theta = 39^\circ\).

$$ A_b = \frac{39}{360} \times \pi \times 10^2 = \frac{3900}{360}\pi = \frac{65}{6}\pi \approx 34.033 \approx 34.0\text{ cm}^2 $$

• Sector c: Sector with \(r = 6\text{ mm}\), \(\theta = 150^\circ\).

$$ A_c = \frac{150}{360} \times \pi \times 6^2 = 15\pi \approx 47.123 \approx 47.1\text{ mm}^2 $$

Calculate areas for sectors d, e, and f

Using the Circle Area knowledge point

• Sector d: Quadrant with \(r = 4\text{ cm}\), \(\theta = 90^\circ\).

$$ A_d = \frac{90}{360} \times \pi \times 4^2 = 4\pi \approx 12.566 \approx 12.6\text{ cm}^2 $$

• Sector e: Sector with \(r = 10.2\text{ mm}\), \(\theta = 104^\circ\).

$$ A_e = \frac{104}{360} \times \pi \times (10.2)^2 = \frac{104 \times 104.04}{360}\pi \approx 30.056\pi \approx 94.425 \approx 94.4\text{ mm}^2 $$

• Sector f: Sector with \(r = 5\text{ m}\), \(\theta = 110^\circ\).

$$ A_f = \frac{110}{360} \times \pi \times 5^2 = \frac{2750}{360}\pi = \frac{275}{36}\pi \approx 23.998 \approx 24.0\text{ m}^2 $$

Answer:

No.	Answer
b	\(34.0\text{ cm}^2\)
c	\(47.1\text{ mm}^2\)
d	\(12.6\text{ cm}^2\)
e	\(94.4\text{ mm}^2\)
f	\(24.0\text{ m}^2\)